In this study, a new technique is considered for solving linear fractional Volterra-Fredholm integro-differential equations (LFVFIDE's) with fractional derivative qualified in the Caputo sense. The method is established in three types of Lagrange polynomials (LP’s), Original Lagrange polynomial (OLP), Barycentric Lagrange polynomial (BLP), and Modified Lagrange polynomial (MLP). General Algorithm is suggested and examples are included to get the best effectiveness, and implementation of these types. Also, as special case fractional differential equation is taken to evaluate the validity of the proposed method. Finally, a comparison between the proposed method and other methods are taken to present the effectiveness of the proposal method in solving these problems.
The laminar fluid flow of water through the annulus duct was investigated numerically by ANSYS fluent version 15.0 with height (2.5, 5, 7.5) cm and constant length (L=60cm). With constant heat flux applied to the outer duct. The heat flux at the range (500,1000,1500,2000) w/m2 and Reynolds number values were ≤ 2300. The problem was 2-D investigated. Results revealed that Nusselt number decrease and the wall temperature increase with the increase of heat flux. Also, the average Nusselt number increase as Re increases. And as the height of the annulus increase, the values of the temperature and the local and average Nusselt number increase.
In this work, a numerical study is performed to predict the solution of two – dimensional, steady and laminar mixed convection flow over a square cylinder placed symmetrically in a vertical parallel plate. A finite difference method is employed to solve the governing differential equations, continuity, momentum, and energy equation balances. The solution is obtained for stream function, vorticity and temperature as dependent variables by iterative technique known as successive over relaxation. The flow and temperature patterns are obtained for Reynolds number and Grashof number at (Re= -50,50,100,-100) (positive or negative value refers to aidding or opposing buoyancy , +1 assisting flow, -1 opposing flow) and (102 to 105) , respective
... Show MoreAllah created the human from clay and made the system of marriage between male
and female as a reason for life continuity and human staying. This system produced an
organization called (the society) which is defined as a group lived in limited time and place.
Islam put fundamental and conditions of the righteous society in the Holy Quran and
prophetic sunna. Islam also put the solutions for problems (if they got) , naturally, these
problems may happened because of the nature of the life.
The problem of the research is summarized by that the problems of the society
enlarged in our Islamic society more than time ago. In the same time , some solution are
imported from west and east and from scientist and ignorant wit
The Electro-Fenton oxidation process is one of the essential advanced electrochemical oxidation processes used to treat Phenol and its derivatives in wastewater. The Electro-Fenton oxidation process was carried out at an ambient temperature at different current density (2, 4, 6, 8 mA/cm2) for up to 6 h. Sodium Sulfate at a concentration of 0.05M was used as a supporting electrolyte, and 0.4 mM of Ferrous ion concentration (Fe2+) was used as a catalyst. The electrolyte cell consists of graphite modified by an electrodepositing layer of PbO2 on its surface as anode and carbon fiber modified with Graphene as a cathode. The results indicated that Phenol concentration decreases with an increase in current dens
... Show MoreThe main object of this study is to solve a system of nonlinear ordinary differential equations (ODE) of the first order governing the epidemic model using numerical methods. The application under study is a mathematical epidemic model which is the influenza model at Australia in 1919. Runge-kutta methods of order 4 and of order 45 for solving this initial value problem(IVP) problem have been used. Finally, the results obtained have been discussed tabularly and graphically.
Wastewater treatment plants operators prefer to make adjustments because they are more cost effective, to use the existing tank instead of building new ones. In this case an imported materials would be used as bio-loads to increase biomass and thus maintain efficiency as the next organic loading increases.In the present study, a local substance "pumice stone" was used as a biological carrier in the aeration tank, and the experiments were carried out in five stages: without biological carriers, filling ratio of 4%,10%,20%, and25% with pumice stone, the maximum organic loading at each stage (1.1884, 1.2144, 1.9432, 2.7768, 3.3141)g BOD /l.d respectively.Other experiments were carried out to determine the best filling ratio, the SS remova
... Show MoreIn the present work, the behavior of thick-walled cylinder of elasto-plastic material (polymeric material) has been studied analytically. The study is based on modified Von-Mises yield criterion (for non metallic material). The equations of stress distribution are obtained for the cylinder under general cases of elastic expansion, plastic initiation and elastic-plastic expansion.
A computer program is developed for evaluating the stress distribution. The solution is carried out for worst boundary conditions when the cylinder is subjected to the combination of pressure load, inertia load, and temperature gradient.
The results are presente
... Show MoreIn this work laser detection and tracking system (LDTS) is designed and implemented using a fuzzy logic controller (FLC). A 5 mW He-Ne laser system and an array of nine PN photodiodes are used in the detection system. The FLC is simulated using MATLAB package and the result is stored in a lock up table to use it in the real time operation of the system. The results give a good system response in the target detection and tracking in the real time operation.
Depletion of fossil fuel is one of the main reasons why the bioethanol has become popular. It is a renewable energy source. In order to meet the great demand of bioethanol, it is best that the bioethanol production is from cheap raw materials. Since the golden shower fruit is not being utilized and is considered as waste material, hence, this study was conducted to make use of the large volume of the residue as feedstock to test its potential for bioethanol extraction.The main goal of this study is to obtain the most volume of bioethanol from the golden shower fruit liquid residue by the factors, days of fermentation (3, 5, and 7 days) and sugar concentration (15, 20 and 25 brix) of the liquid residue. Also, part of the study is to compu
... Show MoreA novel technique Sumudu transform Adomian decomposition method (STADM), is employed to handle some kinds of nonlinear time-fractional equations. We demonstrate that this method finds the solution without discretization or restrictive assumptions. This method is efficient, simple to implement, and produces good results. The fractional derivative is described in the Caputo sense. The solutions are obtained using STADM, and the results show that the suggested technique is valid and applicable and provides a more refined convergent series solution. The MATLAB software carried out all the computations and graphics. Moreover, a graphical representation was made for the solution of some examples. For integer and fractional order problems, solutio
... Show More